From my digging on google... it would appear that mine is a model 780SQ (Squirrel) with a heavy barrel. The remnants of the design carved into the pistol grip portion of the stock lends to it being a squirrel model. And, yes, the two models apparently can share barrels/stocks.
Numrich had what I need to give this poor ol' thing some TLC, although, (unfortunately) the "squirrel" barrel stock was not available. So, a new stock, barrel, barrel retention pin, and front sight group have been ordered. Due to the condition of the barrel before I got it... I'm just gonna swap barrels... even though it is a tack driver (as is).
These are a press fit barrel, but, I'm hoping that securing it into a padded vise and driving the retention pin out is all I'll need to remove/replace the barrel (ok, m'be a plastic faced dead-blow mallet too). I'd also assume that a very thin coat of some anti-seize before installation of the barrel wouldn't be a bad idea?